Go into your Motherboard settings and disable Multi-Threading for your CPU
Also known as Hyperthreading for Intel CPUs
And Simultaneous multithreading for others
Try to make sure Heroes of the Storm is always installed on your C Drive as the game accesses this drive regardless to automatically save files like replays
Right click your C Drive and go into Properties and then Tools
You should see something called Error-checking
Click the Check now button and check BOTH boxes in Check disk options
And click start
Schedule the disk check and then restart your computer
This may take a while but it fixes any software and logic issues that your storage drive has
VERY USEFUL for fixing errors on computers that go through unexpected shutdowns due to power outages or carelessness
This will not fix actual physical damage to your hard drive but will prevent data from being written to the damaged parts in the future
After doing this be sure to Defragment your C Drive as well but SKIP THIS STEP if you are NOT on a Magnetic Hard Disk Drive with actual moving parts
Try running Heroes of the Storm again after this
If issues persist please delete all Blizzard related software and completely reinstall them
This is the best general advice I can give you and I hope this works for you
It should also be known that if you are on weak or faulty hardware you should upgrade as soon as possible for better performance as this game can be highly demanding